engleski

Justification of the dynamic model of curved rods

In this work the asymptotic behaviour of the solution of the evolution problem of three-dimensional linearized elastic curved rod-like bodies with respect to the small thickness l of the rod is analyzed. It is found that, when l tends to zero, the solution converges, in an appropriate sense, to a single space-variable function being an inextensible displacement. Together with an additional function, describing the rotation angle of the cross-sections, it is identified as the unique solution of the one-dimensional evolution problem of curved rods, posed on the middle curve of the rod. The differential equations of the model are obtained.

linearized elasticity; evolution equation; asymptotic analysis; curved rod model

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